Question: (a) Program a calculator or computer to use Eulers method to compute ys1d, where ysxd is the solution of the initial-value problem dy dx 1

(a) Program a calculator or computer to use Euler’s method to compute ys1d, where ysxd is the solution of the initial-value problem dy dx 1 3x2y − 6x2 ys0d − 3 for each of the given step sizes.
(i) h − 1 (ii) h − 0.1 (iii) h − 0.01 (iv) h − 0.001

(b) Verify that y − 2 1 e2x3 is the exact solution of the differential equation.

(c) Find the errors in using Euler’s method to compute ys1d with the step sizes in part (a). What happens to the error when the step size is divided by 10?

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